The incident took place when three tribals were collecting bamboo from a forest in Maldakumar Para village in Dhalai district on Saturday, Dhalai police chief Bijoy Debbarma told IANS.
He said on Saturday night the guerrillas released Dhananjoy Tripura but held back the other two ,Shantijoy Tripura and Manojoy Tripura.
The Border Security Force has asked the Border Guards Bangladesh to take suitable action to rescue the villagers, Debbarma added.
The NLFT, banned in 1997, seeks Tripura's secession from India.
The outfit, whose cadres are hiding mostly in Bangladesh, held two rounds of talks with the central and Tripura governments.